Heinrich Brandt
Encyclopedia
Heinrich Brandt was a German mathematician
who was the first to develop the concept of groupoid
.
Brandt studied at the University of Göttingen and, from 1910 to 1913, at the University of Strasbourg
. In 1912 he attained his doctorate; he was a student of Heinrich Weber
. From 1913 he was assistant at the University of Karlsruhe (TH). He taught geometry
and applied mathematics
from 1921 at RWTH Aachen
. From 1930 he was the chair for mathematics at the University of Halle.
A Brandt matrix is a computational way of describing the Hecke operator
action on theta series as modular form
s. The theory was developed in part by Brandt's student Martin Eichler
. It offers an algorithmic approach for machine computation (in that theta series span spaces of modular forms); the theory is now considered by means of Brandt modules.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who was the first to develop the concept of groupoid
Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be seen as a:...
.
Brandt studied at the University of Göttingen and, from 1910 to 1913, at the University of Strasbourg
University of Strasbourg
The University of Strasbourg in Strasbourg, Alsace, France, is the largest university in France, with about 43,000 students and over 4,000 researchers....
. In 1912 he attained his doctorate; he was a student of Heinrich Weber
Heinrich Weber
Heinrich Martin Weber was a German mathematician. Weber's main work was in algebra, number theory, and analysis...
. From 1913 he was assistant at the University of Karlsruhe (TH). He taught geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
from 1921 at RWTH Aachen
RWTH Aachen
RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....
. From 1930 he was the chair for mathematics at the University of Halle.
A Brandt matrix is a computational way of describing the Hecke operator
Hecke operator
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by , is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations....
action on theta series as modular form
Modular form
In mathematics, a modular form is a analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections...
s. The theory was developed in part by Brandt's student Martin Eichler
Martin Eichler
Martin Eichler was a German number theorist.Eichler received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936....
. It offers an algorithmic approach for machine computation (in that theta series span spaces of modular forms); the theory is now considered by means of Brandt modules.